Modeling Cell Migratory Persistence Through Temporal Correlations And Angular Noise

The persistence of cell migration is a fundamental property of motile behavior, enabling cells to maintain directionality while adapting to fluctuations and external cues. This feature underlies essential processes such as development, immune responses, and cancer invasion. Classical mathematical models have offered key insights into directed migration, yet they often neglect temporal correlations arising from cellular mechanisms that stabilize polarity and protrusion dynamics, processes not well captured by simple white noise. Here, we introduce an agent-based model based on stochastic differential equations (SDEs) that integrates fractional Brownian motion (fBm) to explicitly incorporate translational autocorrelation in cell trajectories. We simulate migration as a function of angular reorientation (Dr) and the strength of correlated noise (H). In this framework, temporal correlation stabilizes trajectory features inherited from initial conditions, whereas angular reorientation introduces variability that enables transitions between erratic and directed motion. Our simulations show that, unlike models driven by white noise, positive correlation markedly enhances persistence even under strong angular reorientation. Moreover, the combination of Dr and H gives rise to emergent behaviors, particularly in the presence of taxis, where persistence and responsiveness are jointly tuned. These results identify correlated noise as a proxy for intrinsic cellular memory and provide a versatile computational framework to interpret the diversity and complexity of migratory behaviors. Significance StatementCell migration drives key biological processes such as immune surveillance, development, and cancer invasion. Most models reduce motility to random walks perturbed by white noise, overlooking temporal correlations that arise from intrinsic cellular memory. By integrating fractional Brownian motion into agent-based modeling, we show how correlated translational noise interacts with angular diffusion to produce emergent behaviors, including overshooting, exploratory loops, and persistent trajectories. Our framework unifies these outcomes under a single mechanistic description and highlights how intrinsic noise modulates taxis, exploration, and persistence. This approach provides mathematicians and cell biologists with a versatile tool to test how cells balance stability and adaptability in dynamic environments.